Frobenius algebras and 2D topological quantum field theories:
This 2003 book describes a striking connection between topology and algebra, namely that 2D topological quantum field theories are equivalent to commutative Frobenius algebras. The precise formulation of the theorem and its proof is given in terms of monoidal categories, and the main purpose of the...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2004
|
| Schriftenreihe: | London Mathematical Society student texts
59 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 UBR01 UBW01 Volltext |
| Zusammenfassung: | This 2003 book describes a striking connection between topology and algebra, namely that 2D topological quantum field theories are equivalent to commutative Frobenius algebras. The precise formulation of the theorem and its proof is given in terms of monoidal categories, and the main purpose of the book is to develop these concepts from an elementary level, and more generally serve as an introduction to categorical viewpoints in mathematics. Rather than just proving the theorem, it is shown how the result fits into a more general pattern concerning universal monoidal categories for algebraic structures. Throughout, the emphasis is on the interplay between algebra and topology, with graphical interpretation of algebraic operations, and topological structures described algebraically in terms of generators and relations. The book will prove valuable to students or researchers entering this field who will learn a host of modern techniques that will prove useful for future work |
| Beschreibung: | 1 Online-Ressource (xiv, 240 Seiten) |
| ISBN: | 9780511615443 |
| DOI: | 10.1017/CBO9780511615443 |
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| 520 | |a This 2003 book describes a striking connection between topology and algebra, namely that 2D topological quantum field theories are equivalent to commutative Frobenius algebras. The precise formulation of the theorem and its proof is given in terms of monoidal categories, and the main purpose of the book is to develop these concepts from an elementary level, and more generally serve as an introduction to categorical viewpoints in mathematics. Rather than just proving the theorem, it is shown how the result fits into a more general pattern concerning universal monoidal categories for algebraic structures. Throughout, the emphasis is on the interplay between algebra and topology, with graphical interpretation of algebraic operations, and topological structures described algebraically in terms of generators and relations. The book will prove valuable to students or researchers entering this field who will learn a host of modern techniques that will prove useful for future work | ||
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Datensatz im Suchindex
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| author | Kock, Joachim |
| author_GND | (DE-588)132344653 |
| author_facet | Kock, Joachim |
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| author_sort | Kock, Joachim |
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| dewey-full | 512/.24 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.24 |
| dewey-search | 512/.24 |
| dewey-sort | 3512 224 |
| dewey-tens | 510 - Mathematics |
| discipline | Physik Mathematik |
| doi_str_mv | 10.1017/CBO9780511615443 |
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| id | DE-604.BV043940946 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:14Z |
| institution | BVB |
| isbn | 9780511615443 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029349915 |
| oclc_num | 967678877 |
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| owner_facet | DE-12 DE-92 DE-355 DE-BY-UBR DE-20 |
| physical | 1 Online-Ressource (xiv, 240 Seiten) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO ZDB-20-CBO UBR Einzelkauf (Lückenergänzung CUP Serien 2018) ZDB-20-CBO UBW_Einzelkauf |
| publishDate | 2004 |
| publishDateSearch | 2004 |
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| publisher | Cambridge University Press |
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| series2 | London Mathematical Society student texts |
| spelling | Kock, Joachim Verfasser (DE-588)132344653 aut Frobenius algebras and 2D topological quantum field theories Joachim Kock Frobenius Algebras & 2-D Topological Quantum Field Theories Cambridge Cambridge University Press 2004 1 Online-Ressource (xiv, 240 Seiten) txt rdacontent c rdamedia cr rdacarrier London Mathematical Society student texts 59 This 2003 book describes a striking connection between topology and algebra, namely that 2D topological quantum field theories are equivalent to commutative Frobenius algebras. The precise formulation of the theorem and its proof is given in terms of monoidal categories, and the main purpose of the book is to develop these concepts from an elementary level, and more generally serve as an introduction to categorical viewpoints in mathematics. Rather than just proving the theorem, it is shown how the result fits into a more general pattern concerning universal monoidal categories for algebraic structures. Throughout, the emphasis is on the interplay between algebra and topology, with graphical interpretation of algebraic operations, and topological structures described algebraically in terms of generators and relations. The book will prove valuable to students or researchers entering this field who will learn a host of modern techniques that will prove useful for future work Frobenius algebras Topological fields Quantum field theory Frobenius-Algebra (DE-588)4155476-0 gnd rswk-swf Topologische Quantenfeldtheorie (DE-588)4426450-1 gnd rswk-swf Frobenius-Algebra (DE-588)4155476-0 s Topologische Quantenfeldtheorie (DE-588)4426450-1 s DE-604 Erscheint auch als Druck-Ausgabe 978-0-521-83267-0 Erscheint auch als Druck-Ausgabe 978-0-521-54031-5 https://doi.org/10.1017/CBO9780511615443 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Kock, Joachim Frobenius algebras and 2D topological quantum field theories Frobenius algebras Topological fields Quantum field theory Frobenius-Algebra (DE-588)4155476-0 gnd Topologische Quantenfeldtheorie (DE-588)4426450-1 gnd |
| subject_GND | (DE-588)4155476-0 (DE-588)4426450-1 |
| title | Frobenius algebras and 2D topological quantum field theories |
| title_alt | Frobenius Algebras & 2-D Topological Quantum Field Theories |
| title_auth | Frobenius algebras and 2D topological quantum field theories |
| title_exact_search | Frobenius algebras and 2D topological quantum field theories |
| title_full | Frobenius algebras and 2D topological quantum field theories Joachim Kock |
| title_fullStr | Frobenius algebras and 2D topological quantum field theories Joachim Kock |
| title_full_unstemmed | Frobenius algebras and 2D topological quantum field theories Joachim Kock |
| title_short | Frobenius algebras and 2D topological quantum field theories |
| title_sort | frobenius algebras and 2d topological quantum field theories |
| topic | Frobenius algebras Topological fields Quantum field theory Frobenius-Algebra (DE-588)4155476-0 gnd Topologische Quantenfeldtheorie (DE-588)4426450-1 gnd |
| topic_facet | Frobenius algebras Topological fields Quantum field theory Frobenius-Algebra Topologische Quantenfeldtheorie |
| url | https://doi.org/10.1017/CBO9780511615443 |
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